Piecewise linear costs

Description

Add a piecewise cost function that steadily increases investment costs with increasing technology rated capacity. This requires the user to switch on the binary purchase decision variable for any relevant technology. Without the purchase decision variable, the technology will have non-zero costs irrespective even if the technology capacity is zero.

New indexed parameters:

• cost_flow_cap_piecewise_slopes (defining the new set pieces)
• cost_flow_cap_piecewise_intercept (defining the new set pieces)

YAML definition

Download the YAML example

variables:
  piecewise_cost_investment:
    description: Investment cost that increases monotonically
    foreach: [nodes, techs, costs]
    where: >
        cost_flow_cap_piecewise_slopes AND cost_flow_cap_piecewise_intercept
        AND purchased_units
    bounds:
      min: 0
      max: .inf

constraints:
  piecewise_costs:
    description: >
      Limit the lower bound of piecewise investment costs to monotonically
      increasing values. Since the model is cost minimising, this is equivalent
      to forcing the investment cost to a specific point along the curve that
      is traced by the superposition of all pieces.
    foreach: [nodes, techs, costs, pieces]
    where: piecewise_cost_investment
    equations:
      - expression: >
          piecewise_cost_investment >=
          sum(cost_flow_cap_piecewise_slopes * flow_cap, over=carriers)
          + cost_flow_cap_piecewise_intercept * purchased_units

# We inject this new source of into the `cost` global expression
global_expressions:
  cost_investment:
    where: >
      (cost_investment_flow_cap OR cost_investment_storage_cap
      OR cost_investment_source_cap OR cost_investment_area_use
      OR cost_investment_purchase OR piecewise_cost_investment)
    equations:
      - expression: >
          $annualisation_weight * (
            $depreciation_rate * (
              sum(default_if_empty(cost_investment_flow_cap, 0), over=carriers) +
              default_if_empty(cost_investment_storage_cap, 0) +
              default_if_empty(cost_investment_source_cap, 0) +
              default_if_empty(cost_investment_area_use, 0) +
              default_if_empty(cost_investment_purchase, 0) +
              default_if_empty(piecewise_cost_investment, 0)
            ) * (1 + cost_om_annual_investment_fraction)
            + sum(cost_om_annual * default_if_empty(flow_cap, 0), over=carriers)
          )